Multilevel Coding for the Full-Duplex Relay Channel

The overwhelming majority of the large literature on coding for the relay channel has been dedicated to the low-SNR regime (binary signaling) and the half- duplex scenario. For non-binary full-duplex signaling, important challenges remain in the simultaneous design of coded modulation at the source and relay. Part of the difficulty is to design the codes with the requisite correlation prescribed by theory. This paper proposes a systematic code design methodology for the relay channel via multilevel coding (MLC). The main difficulty was that a straightforward extension of the chain rule MLC decomposition, as was previously used in the point to-point MLC, would result in many dependencies between the coded layers of the source and relay. A key contribution of this paper is showing that MLC joint source/relay code design can be implemented via standard binary code design procedures. Specifically, we outline a design process where the correlation between the source and relay codes are implemented purely via pairwise correlations between the binary codes of source and relay at each layer, without any other inter-layer correlations. Moreover, a specific design example is provided via a simple XOR operation on two conventionally designed codes. Numerical results show excellent performance for the proposed scheme.